Print Run Of Reasonable Astronomy In Ancient Comparative Study

The Exchange between ancient China and India began from the Western Han Dynasty and reached the summit in the Tang Dynasty. The historians of science are paying a good deal of attention to the research on the mathematical astronomy between the two countries in ancient times. Based on the research of other scholars, some concrete problems in terms of the mathematical astronomy between the two countries have discussed including the general picture of the Indian mathematical astronomy and the theories of the precession of the equinoxes, the solar shadows and the water clock. The paper consists of five parts. Part one based on the historical background of the exchange between the two countries, studies the development of the Indian mathematical astronomy, which was influenced by the Babylon, Greece and Arab countries. The contents of Indian astronomy were introduced into China in the Sui and Tang Dynasty.Part two studies the Indian sine tables. Analyzed the constructive methods and characteristics of the Indian sine tables in 5~18 century. Pointed out the Indian sine tables are noted for the influence of Greek chord tables and have their own creativities. The Indian sine table was introduced into China by Qutan Xida in the Jiuzhi Calendar, but it did not produce influence to the mathematical astronomy in ancient China.Part three deals with the understanding about the precession of the equinoxes. Research centers on the four heart aspects about contentious problem of the precession of the equinoxes in China. Compared the similarities and differences on the cognition of the precession of the equinoxes in the two countries.Part four based on circumspect interpretation of relevant texts in the calendars from the Tang Dynasty to the Yuan Dynasty, the principles and characteristics of the algorithm for calculating solar shadows in Jiu Fu are verified. In the Qintian Calendar, by taking advantage of the result of Yi Xing's meridian survey during the Kaiyuan period of the Tang Dynasty, Wang Pu proposed a particular formula of solar shadows in Jiu Fu, from which the first expression of tangent function in the history of mathematical astronomy can be drawn.Part five researches the core algorithm of methods for calculating solar shadows and water clock in ancient China's calendar. Xiaoxitonglü in the Dayan Calendar was also known as Xiaoxidingshu or Xiaoxishu in later calendars. It was a fundamental element of methods for calculating solar shadows and water clock. Revealed the core algorithm's signification in mathematical astronomy.